Purpose: Four-dimensional (4D) cone-beam computed tomography (CBCT) of the lung is an effective tool for motion management in radiotherapy but presents a challenge because of slow gantry rotation times. Sorting the individual projections by breathing phase and using an established technique such as Feldkamp–Davis–Kress (FDK) to generate corresponding phase-correlated (PC) three-dimensional (3D) images results in reconstructions (FDK-PC) that often contain severe streaking artifacts due to the sparse angular sampling distributions. These can be reduced by further slowing down the gantry at the expense of incurring unwanted increases in scan times and dose. A computationally efficient alternative is the McKinnon-Bates (MKB) reconstruction algorithm that has shown promise in reducing view aliasing-induced streaking but can produce ghosting artifacts that reduce contrast and impede the determination of motion trajectories. The purpose of this work was to identify and correct shortcomings in the MKB algorithm. Methods: In the general MKB approach, a time-averaged 3D prior image is first reconstructed. The prior is then forward-projected at the same angles as the original projection data creating time-averaged reprojections. These reprojections are subsequently subtracted from the original (unblurred) projections to create motion-encoded difference projections. The difference projections are reconstructed into PC difference images that are added to the well-sampled 3D prior to create the higher quality 4D image. The cause of the ghosting in the traditional 4D MKB images was studied and traced to motion-induced streaking in the prior that, when reprojected, has the undesirable effect of re-encoding for motion in what should be a purely time-averaged reprojection. A new method, designated as the modified McKinnon-Bates (mMKB) algorithm, was developed based on destreaking the prior. This was coupled with a postprocessing 4D bilateral filter for noise suppression and edge preservation (mMKBbf). The algorithms were tested with the 4D XCAT phantom using four simulated scan times (57, 60, 120, 180 s) and with two in vivo thorax studies (acquisition time of 60 and 90 s). Contrast-to-noise ratios (CNRs) of the target lesions and overall visual quality of the images were assessed. Results: Prior destreaking (mMKB algorithm) reduced ghosting artifacts and increased CNRs for all cases, with the biggest impacts seen in the end inhale (EI) and end exhale (EE) phases of the respiratory cycle. For the XCAT phantom, mMKB lesion CNR was 44% higher than the MKB lesion CNR and was 81% higher than the FDK-PC lesion CNR (EI and EE phases). The bilateral filter provided a further average CNR improvement of 87% with the highest increases associated with longer scan times. Across all phases and scan times, the maximum mMKBbf-to-FDK-PC CNR improvement was over 300%. In vivo results agreed with XCAT results. Significantly less ghosting was observed throughout the mMKB images including near the lesions-of-interest and the diaphragm allowing for, in one case, visualization of a small tumor with nearly 30 mm of motion. The maximum FDK-PC-to-MKBbf CNR improvement for Patient 1's lesion was 261% and for Patient 2's lesion was 318%. Conclusions: The 4D mMKB algorithm yields good quality coronal and sagittal images in the thorax that may provide sufficient information for patient verification.